Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential

被引：0

作者：

Pei, Shuaichao ^{[1
]}

Hou, Yanren ^{[1
]}

Yan, Wenjing ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 38卷 / 01期

基金：

中国国家自然科学基金;

关键词：

invariant energy quadratization; modified phase field crystal model; unconditional energy stability; vacancy; FINITE-DIFFERENCE SCHEME; DISCONTINUOUS GALERKIN METHOD; TIME-STEPPING STRATEGY; ENERGY STABILITY; CONVERGENCE ANALYSIS; SPLITTING METHODS; LINEAR SCHEMES; SAV APPROACH; ALLEN-CAHN; 2ND-ORDER;

D O I：

10.1002/num.22828

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider numerical approximations for a modified phase field crystal model with a strong nonlinear vacancy potential. Based on the invariant energy quadratization approach and stabilized strategies, we develop linear, unconditionally energy stable numerical schemes using the first-order Euler method, the second-order backward differentiation formulas and the second-order Crank-Nicolson method, respectively. We rigorously prove the unconditional energy stability, the mass conservation of these three numerical schemes and carry out error estimates in time for the first-order numerical scheme. Various numerical experiments in 2D and 3D are carried out to validate the accuracy, energy stability, mass conservation, and efficiency of the proposed schemes.

引用

页码：65 / 101

页数：37

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